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Tight upper and lower bounds for energy eigenvalues of the Schrödinger equation

Francisco M. Fernández, Q. Ma, and R. H. Tipping
Phys. Rev. A 39, 1605 – Published 1 February 1989
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Abstract

A method is presented for the calculation of tight upper and lower bounds for the energy eigenvalues of the Schrödinger equation. The method is based on a rational functional approximation for the series expansion of the solution of the Riccati equation for the logarithmic derivative of the wave function. Specific applications for one-dimensional anharmonic oscillators and for the Yukawa potential are given, and the present results are compared with those obtainable by other procedures.

  • Received 12 July 1988

DOI:https://doi.org/10.1103/PhysRevA.39.1605

©1989 American Physical Society

Authors & Affiliations

Francisco M. Fernández

  • Instituto de Investigationes Fiscoquímicas Teóricas y Aplicadas, División Química Teórica, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina

Q. Ma and R. H. Tipping

  • Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487

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Vol. 39, Iss. 4 — February 1989

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